story
Contribution: there are platforms who already uses WebRTC instead of rtmp to stream the live camera feed. You can use tokbox's apis for example.
Delivery: This is where it gets more tricky, the nice thing about http based streaming like HLS and DASH is that it's cacheable just like any other file served over http - making it extremely scalable and that's how most CDNs operate today. Changing that part into WebRTC has it's benefits like low latency but has a huge degradation in scaling complexity because of the connection state oriented nature of WebRTC, there are companies trying to build that as well e.g: Red5
The main reasons for transcoding are downstream bandwidth usage and codec support. WebRTC mandates VP8, so codecs shouldn't be an issue. Downstream bandwidth usage probably wouldn't be a major concern when it's viable to stream at 1080p to thousands of viewers from a home connection (though I doubt that's going to happen soon). So you could probably ignore transcoding entirely.
However, marketing would probably be an issue, since this architecture would prevent streamers from having more than about a hundred watchers, meaning that the big fish would stick to Twitch. That said, I suppose you could have a failover system, where larger streamers would switch to a relay-based system.